We address in this paper the problem of blow molding for a polymer exhibiting a
deformation induced crystallization (e.g. Poly EthyleneTerephthalate or PET). In a first part,
we give the equations of a model that couples the mechanics to the crystallization for a class
of molecular models (e.g. Maxwell or POM-POM models). In a second part, without a real
stabilities analysis, we follow the Swift analysis for biaxial deformations. We conclude this
study in showing that it is possible to quantify how crystallization during the process
stabilizes it. In enhancing strongly the strain hardening, crystallization is namely a stability
factor against necking.